Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Removing point singularities of Riemannian manifolds


Authors: P. D. Smith and Deane Yang
Journal: Trans. Amer. Math. Soc. 333 (1992), 203-219
MSC: Primary 53C21; Secondary 53C22
MathSciNet review: 1052910
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the behavior of geodesics passing through a point singularity of a Riemannian manifold. In particular, we show that if the curvature does not blow up too rapidly near the singularity, then the singularity is at worst an orbifold singularity. The idea is to construct the exponential map centered at a singularity. Since there is no tangent space at the singularity, a surrogate is needed. We show that the vector space of radially parallel vector fields is well defined and that there is a correspondence between unit radially parallel vector fields and geodesics emanating from the singular point.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 53C21, 53C22

Retrieve articles in all journals with MSC: 53C21, 53C22


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1052910-2
PII: S 0002-9947(1992)1052910-2
Article copyright: © Copyright 1992 American Mathematical Society